The present invention relates to equalizers for receivers of wireless communication systems and more particularly to receiver equalizers more commonly known as blind channel equalizers. This invention also relates to methods of blind channel equalization for receivers in wireless communication.
xe2x80x98Channel Equalizationxe2x80x99 generally refers to signal equalization techniques which do not require prior characterization of the transmission channel as a pre-requisite for satisfactory signal recovery. Equalization is always necessary in wireless communication to remove or alleviate signal contamination during transmission, for example, by co-channel interference (CCI) or inter-symbol interference (ISI).
The potential application of blind channel equalization techniques in wireless communication has made them one of the most active areas of research in recent years. Initial studies of blind equalization have been concentrated on single input systems but there are now increasing interests in blind channel equalization in multiple-input and multiple-output (MIMO) systems. Algorithms based only on second order statistics (xe2x80x9cSOSxe2x80x9d) of the received signals are attractive because of their simplicity and low requirement on processing power. For these reasons, it would be desirable to develop SOS-based blind channel equalizing for MIMO systems.
Known blind channel-equalization algorithms are typically based on second- and higher-order statistics of the received signals. Recent research developments have shown that blind channel equalization can be successfully done in single-input, multiple-output (xe2x80x9cSIMOxe2x80x9d) systems relying only on second-order statistics of the received signals provided that there is sufficient receiver signal diversity. This requirement means that the receiver output channels must be diverse enough to share no common zeroes (see for example, L. Tong, et. al, xe2x80x9cBlind Channel Identification Based on Second-Order Statistics: A Frequency Domain Approachxe2x80x9d IEEE Trans. on Information Technology, no.1, pp.329-334, Mar. 1995xe2x80x9d). It is also appreciated that many of the known algorithms for blind channel-equalization in SIMO systems can be generalized to MIMO systems as long as the virtual users at the transmitter input is smaller than the number of virtual output at the receiving end of the transmission system.
It is well-known that the performance of SOS-based ISI equalizing algorithms rely critically on channel diversity, which is usually achieved either by antenna diversity or by over-sampling of output signals when the channels have excess bandwidth. Blind channel identification is no longer possible with SOS based algorithms alone and higher order statistics (xe2x80x9cHOSxe2x80x9d) are often required to compensate for the loss of information when there are common, or near common, zeroes among the diversity channels. Therefore, known blind equalization algorithms for ISI suppression used in MIMO systems are hitherto typically based on both SOS and HOS of the received signals.
Another major drawback of pure SOS based equalizing algorithms is their sensitivity towards variation in channel order estimate, since it is well known that accurate channel estimate is difficult to achieve. Poor blind channel identification will inevitably result unless there is an accurate channel order estimate.
Furthermore, while it is common knowledge that blind channel identification can be performed in blind equalizing receiver systems before actual signal reception, it is well-known that channel estimation errors tend to be magnified by linear equalizers and is therefore not desirable for linear MIMO systems.
It is therefore an object of the present invention to provide blind equalizers and methods for blind equalization for wireless communication which are primarily based on second-order statistics of the received signals. It is also an object that such blind equalizers or equalization methods are operable without the need of channel identification information and are less sensitive to channel order estimates which is a drawback common to most known SOS based blind equalizing receiver.
According to the present invention, there is provided a signal equalization method for a multiple-input, multiple-output (MIMO) wireless communication system in which the wireless channel of the communication system can be modeled by a finite-impulse-response (FIR) system of order integer M. The communication system is provided with system diversity having a receiver diversity factor of integer N. The equalization method includes the steps of devising a system convolution matrix A, wherein said matrix A is a generalized Sylvester matrix comprising (L+1) block rows and (M+L+1) block columns of sub-matrices each of which block is a matrix of dimension Nxc3x97d, wherein the number of rows of A, being the product N and (L+1), is made to exceed the number of columns of A, being product of d and (M+L+1), by selecting an appropriate integer L, said matrix A relates a vector of sampled channel output signals o(m) to a vector of corresponding input signal symbol sequences, s(m), transmitted by a plurality (d) of users at the transmitting end of said transmission system by the relationship o(m)=A s(m), wherein o(m) is a vector comprising a selected sampled channel output signal vector (y(m)) and a plurality (L) of sampled channel output signals ([y(mxe2x88x921), . . . , y(mxe2x88x92L)]) which immediately precede said selected sampled channel output signal y(m), each said sampled channel output signal is a Nxc3x971 vector due to system diversity; calculating second order statistics of said vector of sampled channel output signals o(m); selecting suitable linear equalizing functions (G) derived from said second order statistics of said sampled channel output signals; and algebraically operating the said vector of sampled channel output signals o(m) by said linear equalizing functions, said algebraic operations are selected so that the results of such operation are equivalent to removing inter-symbol interference elements from said matrix A by forcing all block columns of the matrix A to zero except for a specific block column of A.
Preferably, the aforementioned second order statistics are the auto-covariance, R(k), where k is a natural number, of the received and sampled channel output signals, o(m).
Preferably, the suitable linear function G is obtained by multiplying the auto-covariance R(k) of the received and sampled channel output signals, o(m), by the pseudo-inverse of the auto-covariance of R(O) and is equal to R(k)R(o)#, said equalized received signals are then obtained by multiplying said sampled channel output signals, o(m), by said linear function with k=M+L.
According to a second aspect of the present invention, there is provided a receiver equalizer for a multiple-input, multiple-output (MIMO) wireless communication system in which the wireless channel of said communication system being modeled by a finite-impulse-response (FIR) system of order integer M, said communication system is provided with system diversity having a receiver diversity factor of integer N. The equalizer includes means for devising a system convolution matrix A, wherein said matrix A is a generalized Sylvester matrix comprising (L+1) block rows and (M+L+1) block columns of sub-matrices each of which block is a matrix of dimension Nxd, wherein the number of rows of A, being the product of N and (L+1), is made to exceed the number of columns of A, being the product of d and (M+L+1), by selecting an appropriate integer L, said matrix A relates a vector of sampled channel output signals o(m) to a vector of corresponding input signal symbol sequences, s(m), transmitted by a plurality (d) of users at the transmitting end of said transmission system by the relationship o(m)=A s(m), wherein o(m) is a vector comprising a selected sampled channel output signal vector (y(m)) and a plurality (L) of sampled channel output signals which immediately precede said selected sampled channel output signal y(m), each said sampled channel output signal is a Nxc3x971 vector due to system diversity; means for calculating second order statistics of said vector of sampled channel output signals o(m); means for selecting suitable linear equalizing functions (G) derived from said second order statistics of said sampled channel output signals; and means for algebraically operating said vector of sampled channel output signals o(m) by said linear equalizing functions, said algebraic operations are selected so that the results of such operation are equivalent to removing inter-symbol interference elements from said matrix A by forcing all block columns of the matrix A to zero except for a specific block column of A.
According to another aspect of the present invention, there is provided a multiple-input multiple-output wireless communication system, in which the wireless channel of said communication system can be modeled by a finite-impulse-response (FIR) system of order integer M, comprising means for transmitting symbol sequences from a plurality (d) of users at the transmitting end of said system through the said wireless channel; means for receiving said symbol sequences transmitted from said plurality of users with receiver diversity means characterized by a diversity factor of integer N, so that N sets of sampled channel signal outputs corresponding to said symbol sequences are available; means for equalizing said received sampled channel signal outputs with intent to remove ISI wherein said equalizing means comprises means for devising a system convolution matrix A, wherein said matrix A is a generalized Sylvester matrix comprising (L+1) block rows and (M+L+1) block columns of sub-matrices each of which block is a matrix of dimension Nxd, wherein the number of rows of A, being the product of N and (L+1), is made to exceed the number of columns of A, being the product of d and (M+L+1), by selecting an appropriate integer L, said matrix A relates a vector of sampled channel output signals o(m) to a vector of corresponding input signal symbol sequences, s(m), transmitted by a plurality (d) of users at the transmitting end of said transmission system by the relationship o(m)=A s(m), wherein o(m) is a vector comprising a selected sampled channel output signal vector (y(m)) and a plurality (L) of sampled channel output signals ([y(mxe2x88x921), . . . , y(mxe2x88x92L)]) which immediately precede said selected sampled channel output signal y(m), each said sampled channel output signal is a Nxc3x971 vector due to system diversity; means for calculating second order statistics of said vector of sampled channel output signals o(m); means for selecting suitable linear equalizing functions (G) derived from said second order statistics of said sampled channel output signals; and means for algebraically operating said vector of sampled channel output signals o(m) by said linear equalizing functions, said algebraic operations are selected so that the results of such operation are equivalent to removing inter-symbol interference elements from said matrix A by forcing all block columns of the matrix A to zero except for a specific block column of A.
According to a further aspect of the present invention, there is provided a method of multiple-input multiple-output communication in a wireless channel, which channel can be modeled by a finite-impulse-response (FIR) system of order integer M, said method comprising transmitting symbol sequences from a plurality (d) of users at the transmitting end of said system through said wireless channel; receiving said symbol sequences transmitted from said plurality of users by a receiver with system diversity characterized by a diversity factor of integer N, so that N sets of sampled channel signal outputs corresponding to said symbol sequences are available; equalizing said received sampled channel signal outputs with intent to remove ISI wherein said equalizing comprises devising a system convolution matrix A, wherein said matrix A is a generalized Sylvester matrix comprising (L+1) block rows and (M+L+1) block columns of sub-matrices each of which block is a matrix of dimension Nxd, wherein the number of rows of A, being the product N and (L+1), is made to exceed the number of columns of A, being the product d and (M+L+1), by selecting an appropriate integer L, said matrix A relates a vector of sampled channel output signals o(m) to a vector of corresponding input signal symbol sequences, s(m), transmitted by a plurality (d) of users at the transmitting end of said transmission system by the relationship o(m)=A s(m), wherein o(m) is a vector comprising a selected sampled channel output signal vector (y(m)) and a plurality (L) of sampled channel output signals which immediately precede said selected sampled channel output signal y(m), each said sampled channel output signal is a Nxc3x971 vector due to system diversity; calculating second order statistics of said vector of sampled channel output signals o(m); selecting suitable linear equalizing functions (G) derived from said second order statistics of said sampled channel output signals; and means for algebraically operating said vector of sampled channel output signals o(m) by said linear equalizing functions, said algebraic operations are selected so that the results of such operation are equivalent to removing inter-symbol interference elements from said matrix A by forcing all block columns of the matrix A to zero except for a specific block column of A.